Subgroups — C₁₃×C₂₉×C₆₄ #72201413

Order 24128.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₂₉×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₁₆×C₂₉	C₄	1	1	yes	characteristic
3	C₈×C₁₃×C₂₉	C₈	1	1	yes	characteristic
4	C₂₉×C₆₄	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₄×C₁₃×C₂₉	C₁₆	1	1	yes	characteristic
6	C₂₉×C₃₂	C₂×C₁₃	1	1	yes	characteristic
7	C₁₃×C₆₄	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₁₃×C₂₉	C₃₂	1	1	yes	characteristic
9	C₁₆×C₂₉	C₄×C₁₃	1	1	yes	characteristic
10	C₁₃×C₃₂	C₂×C₂₉	1	1	yes	characteristic
11	C₁₃×C₂₉	C₆₄	1	1	yes	characteristic, direct product factor, Hall
12	C₈×C₂₉	C₈×C₁₃	1	1	yes	characteristic
13	C₁₃×C₁₆	C₄×C₂₉	1	1	yes	characteristic
14	C₄×C₂₉	C₁₃×C₁₆	1	1	yes	characteristic
15	C₈×C₁₃	C₈×C₂₉	1	1	yes	characteristic
16	C₆₄	C₁₃×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₂₉	C₁₃×C₃₂	1	1	yes	characteristic
18	C₄×C₁₃	C₁₆×C₂₉	1	1	yes	characteristic
19	C₃₂	C₂×C₁₃×C₂₉	1	1	yes	characteristic
20	C₂₉	C₁₃×C₆₄	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×C₁₃	C₂₉×C₃₂	1	1	yes	characteristic
22	C₁₆	C₄×C₁₃×C₂₉	1	1	yes	characteristic
23	C₁₃	C₂₉×C₆₄	1	1	yes	characteristic, direct product factor, Sylow
24	C₈	C₈×C₁₃×C₂₉	1	1	yes	characteristic
25	C₄	C₁₃×C₁₆×C₂₉	1	1	yes	characteristic
26	C₂	C₁₃×C₂₉×C₃₂	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.